CP-ROC bands improve graph classification accuracy and uncertainty quantification.
problem Uncertainty quantification and robustness to distributional shifts in graph classification.
method Conditional Prediction ROC (CP-ROC) bands for graph classification, developed for TGNNs and adaptable to GNNs.
result Statistically guaranteed coverage for CP-ROC under local exchangeability condition, improving prediction reliability.
CUQ-GNN adapts uncertainty quantification for graph data, improving on GPN.
problem Defining meaningful uncertainty on graph data with domain-specific characteristics.
method Combines Graph Neural Networks with Posterior Networks using Normalizing Flows.
result CUQ-GNN produces more flexible and effective uncertainty estimates.
ProDAG uses variational inference to learn DAGs with uncertainty quantification.
problem Statistical and computational challenges in learning a single DAG from data.
method Bayesian variational inference framework with novel distributions.
result ProDAG outperforms state-of-the-art alternatives in accuracy and uncertainty quantification.
New method adapts to structural shifts in graph data for better label prevalence estimation.
problem Structural shifts in graph data affect label prevalence estimation.
method Importance sampling variant of KDEy quantification approach.
result Adapts to structural shifts and outperforms standard approaches.
PE-GQNN improves spatial data prediction and uncertainty quantification.
problem Poor calibration of predictive distributions in spatial data models.
method Combines PE-GNNs with Quantile Neural Networks and recalibration techniques.
result PE-GQNN outperforms existing methods in predictive accuracy and uncertainty quantification.
Bayesian graph contrastive learning improves uncertainty quantification for graph analytics.
problem Uncertainty quantification for node representations in graph contrastive learning.
method Proposes a Bayesian framework to learn stochastic encoders representing nodes as distributions, providing uncertainty estimates.
result Significant improvement in performance on benchmark datasets compared to existing methods.
The study analyzes and benchmarks graph conformal prediction methods.
problem Uncertainty quantification in graph node classification.
method Analysis and scaling of existing graph conformal prediction methods.
result Justified recommendations for future graph conformal prediction research.
BayesIMP combines multiple causal graphs to estimate average treatment effects with uncertainty.
problem Uncertainty quantification in causal inference from multiple datasets.
method Bayesian Interventional Mean Processes (BayesIMP) integrating probabilistic integration and kernel mean embeddings.
result Improvements in average treatment effect estimation over state-of-the-art methods.
Paper tackles uncertainty in GNNs for graph data.
problem Uncertainty in GNNs' predictions for graph data.
method CF-T2NN, tensor decomposition, topological learning.
result CF-T2NN improves reliability and interpretability of GNN outcomes.
A new method reduces complexity and uncertainty in neural networks.
problem Uncertainty quantification in complex neural networks.
method Condensed Stein Variational Gradient Descent (cSVGD) method.
result Condensed SVGD provides uncertainty quantification on parameters.
BSG learns dynamic network spillovers and uncertainty quantification.
problem Identifying indirect spillovers and systemic risk in dynamic networks.
method Bayesian Spillover Graphs using FEVD and Bayesian time series models.
result Significant performance gains over baselines in identifying source and sink nodes.
A scalable GP model for online uncertainty quantification over graphs.
problem Scalable uncertainty quantification over graphs with dynamic data.
method Graph-aware parametric Gaussian process model using random features and online conformal prediction.
result Improved coverage and efficient prediction sets over existing methods.
Hybrid model integrates GATv2 and geostatistics for better spatial prediction and uncertainty.
problem Accurate spatial prediction and uncertainty quantification in epidemiology and risk analysis.
method Integrates Graph Attention Network (GATv2) with model-based geostatistics (MBG) to capture relational and spatial dependencies.
result Hybrid model improves predictive accuracy and uncertainty quantification compared to standalone models.
The paper improves uncertainty quantification for node classification using distance-based regularization.
problem Uncertainty in deep learning models, especially for node classification tasks.
method Graph posterior networks (GPNs) with UCE loss function, followed by a distance-based regularization.
result The proposed distance-based regularization outperforms state-of-the-art methods in OOD detection and misclassification detection.
New framework models epistemic uncertainty in GNNs using random sets.
problem Uncertainty in graph neural network predictions.
method Introduces a belief function (random set) approach to model epistemic uncertainty in GNNs.
result Demonstrates superior uncertainty quantification on various graph datasets.
The paper develops a method to discover causal relations and predict material laws with uncertainty quantification.
problem Discovering causal relations and predicting material laws with uncertainty in civil engineering applications.
method The paper develops a causal discovery algorithm to infer causal relations among time-history data. It uses a deep neural network with dropout layers for uncertainty quantification and propagates predictions through a causal graph.
result The method accurately predicts material laws and quantifies uncertainty, as demonstrated in two numerical examples.
Method learns Dirichlet-to-Neumann maps on graphs using Gaussian processes.
problem Coupling multiphysics simulations on graphs with conservation constraints.
method Gaussian processes combined with discrete exterior calculus and maximum likelihood estimation.
result Data-driven predictions with uncertainty quantification on entire graph.
Machine learning combines high- and low-fidelity models for efficient uncertainty quantification and optimization.
problem Efficiently combining high- and low-fidelity models for uncertainty quantification and optimization.
method Machine learning-based multi-fidelity methods for uncertainty quantification and optimization.
result Unified perspective on multi-fidelity priors for optimization.
GraphPPD models graph-level uncertainty using GNN embeddings.
problem Capturing uncertainty in graph-level predictions.
method Variational modelling for posterior predictive distribution.
result Effective uncertainty-aware predictions on graph-level tasks.
Novel framework for uncertainty quantification in metric spaces.
problem Uncertainty quantification in regression models with metric responses.
method Developed algorithms for large datasets, agnostic to predictive models, with asymptotic and non-asymptotic guarantees.
result Asymptotic and non-asymptotic guarantees for special cases, demonstrated in clinical applications.
Develops a framework for inferring causal relationships in networked data with uncertainty quantification.
problem Extracting reliable inference from complex Hawkes network data with uncertainty.
method Statistical inference framework based on maximum likelihood estimation and concentration inequalities of continuous-time martingales.
result Provides a non-asymptotic confidence set for uncertainty quantification.
Method quantifies uncertainties in complex MRF models.
problem Uncertainties in MRF predictions due to data, modeling, and approximations.
method Information-based uncertainty quantification using MRF graphical structure.
result Tight bounds on predictions for quantities of interest in MRFs.
Paper quantifies uncertainty in pairwise comparison models.
problem Uncertainty quantification in sparse Bradley-Terry-Luce models.
method Unified proof strategy for MLE and spectral estimator.
result Sharp and uniform non-asymptotic expansions for estimators.
GEBM improves uncertainty quantification in graph neural networks.
problem Challenges in quantifying epistemic uncertainty in graph neural networks.
method Energy-based model (EBM) that aggregates uncertainty at different structural levels.
result Significantly improves predictive robustness and achieves best separation of in-distribution and out-of-distribution data.
CF-GNN provides reliable uncertainty estimates for graph data.
problem Lack of rigorous uncertainty estimates in GNNs.
method Conformal prediction extended to graph-based models (CF-GNN).
result CF-GNN produces prediction sets with provable coverage probability.
Proposes SDE framework for uncertainty quantification in graph neural networks.
problem Lack of uncertainty quantification in graph neural networks.
method Introduces Latent Graph Neural Stochastic Differential Equations (LGNSDE) with Bayesian prior-posterior mechanism and Brownian motion.
result LGNSDEs provide theoretically sensible guarantees for uncertainty estimates and are robust to perturbations.
We introduce vine computational graphs for efficient ML integration of vine copulas.
problem Integrating vine copulas into modern machine learning pipelines.
method Developed vine computational graphs and algorithms for conditional sampling, scheduling, and structure construction.
result Gradient flow through vine copulas improves performance in machine learning models.
A method for predicting signals on graphs using Gaussian processes and optimal transport.
problem Predicting signals on complex, graph-based inputs with uncertainty quantification.
method Combining regularized optimal transport, dimension reduction, and Gaussian processes indexed by graphs.
result Efficient prediction of signals on graphs with confidence intervals.
Proposes a probabilistic framework for smart contract risk quantification.
problem Quantifying financial risk of smart contract cyber attacks and failures.
method Probabilistic graph-theoretical framework using bond percolation models.
result Analytical results and numerical examples for aggregate loss distribution.
A new conformal prediction framework for graph-valued outputs using Z-Gromov-Wasserstein distances.
problem Lack of principled uncertainty quantification for graph-valued supervised prediction.
method Proposes a conformal prediction framework using Z-Gromov-Wasserstein distances for graph-valued outputs.
result Provides distribution-free coverage guarantees for graph-valued outputs.
Classification of high dimensional data finds wide-ranging applications. In many of these applications equipping the resulting classification with a measure of uncertainty may be as important as the classification itself. In this paper we introduce, develop algorithms for, and investigate the properties of, a variety o…
Bayesian neural networks learn graph structure with interpretable parameters.
problem Learning graph structure from nodal observations in data with uncertainty.
method Introduces novel iterations with independently interpretable parameters and Bayesian neural networks.
result Bayesian neural networks provide well-calibrated uncertainty quantification on graph structure.
GeometricKernels package implements kernels for uncertain data on graphs, manifolds, and meshes.
problem Defining and computing kernels for structured data on graphs, manifolds, and meshes.
method Implementation of geometric analogs of Euclidean kernels (heat and Matérn) with automatic differentiation support.
result Ability to compute Fourier-feature-type expansions on geometric spaces.
Graph Posterior Network improves uncertainty estimation for node classification in interdependent graphs.
problem Uncertainty quantification for non-independent node-level predictions in graphs.
method Derives axioms for expected predictive uncertainty, proposes Graph Posterior Network (GPN) which performs Bayesian posterior updates.
result GPN outperforms existing approaches for uncertainty estimation in semi-supervised node classification.
New model predicts travel demand uncertainty with high accuracy.
problem Uncertainty and sparsity in sparse travel demand prediction.
method Spatial-Temporal Zero-Inflated Negative Binomial Graph Neural Network (STZINB-GNN).
result STZINB-GNN outperforms benchmarks in predicting travel demand uncertainty.
STOIC improves energy demand forecasting with reliable uncertainty estimates.
problem Accurate point forecasts alone are insufficient for energy systems; reliable uncertainty estimates are needed.
method Integrates graph-based forecasting with tabular foundation models for zero-shot calibration of spatial-temporal residuals.
result STOIC delivers more reliable and robust uncertainty estimates for complex graph-structured energy time series.
The paper introduces algorithms for uncertainty quantification in metric spaces.
problem Uncertainty quantification in regression models defined on metric spaces.
method Proposes conformal and kNN prediction algorithms for metric spaces.
result Both algorithms provide finite-sample guarantees and improve local coverage calibration.
BetaExplainer improves GNN interpretability by masking unimportant edges.
problem Interpreting GNNs' predictions is difficult due to black-box behavior and lack of uncertainty quantification.
method BetaExplainer uses a sparsity-inducing prior to mask unimportant edges during training.
result BetaExplainer provides uncertainty in edge importance and improves predictive accuracy on challenging datasets.
Proposes a new model to predict travel demand with zero-inflated and long-tail characteristics.
problem Sparse and long-tailed travel demand data with many zeros.
method Spatial-Temporal Tweedie Graph Neural Network (STTD) using Tweedie distribution.
result STTD provides accurate predictions and precise confidence intervals.
Prob-GNN quantifies travel demand uncertainty with deep learning.
problem Uncertainty in travel demand prediction.
method Probabilistic Graph Neural Networks (Prob-GNN) framework.
result Probabilistic assumptions significantly impact uncertainty prediction.
New method improves uncertainty estimation in complex statistical models.
problem Challenges in estimating high-dimensional mixed models due to computational complexity.
method Partially factorized variational inference to relax mean-field assumption.
result Relaxed variational inference provides accurate uncertainty quantification without high computational cost.
Graph neural networks extend neural Bayes estimators to irregular spatial data.
problem Estimating parameters from irregular spatial data with computational efficiency.
method Employing graph neural networks to approximate Bayes estimators for irregular spatial data.
result Extending neural Bayes estimation to irregular spatial data with computational benefits.
Improves GNN prediction sets with conformal prediction for node classification.
problem Lack of predictive uncertainty for GNN models.
method Adapted conformal prediction for graph data, weighting scores based on graph structure.
result Better calibrated and tighter prediction sets than naive conformal prediction.
Bayesian GNNs with temperature improve prediction efficiency in CP.
problem Efficiency of prediction sets in CP for GNNs.
method Introducing a temperature parameter into Bayesian GNNs within the CP framework.
result More efficient prediction sets achieved with the temperature parameter.
Simplified MDNs quantify uncertainty in large complex datasets.
problem Uncertainty quantification in large scale complex data.
method Simplified Mixture Density Networks (MDNs) for regression problems.
result Improved predictive log-likelihood and root-mean-square-error compared to existing methods.
This paper studies uncertainty quantification in deep spatiotemporal forecasting.
problem Uncertainty quantification in deep spatiotemporal forecasting models.
method Analysis of UQ methods from Bayesian and frequentist perspectives, including statistical decision theory.
result Different UQ methods have different strengths and weaknesses, with Bayesian methods being more robust in mean prediction and frequentist methods providing more extensive coverage.
We introduce a model for causal structure learning from multivariate functional data, even when graphs have cycles.
problem Discovering causal relationships from multivariate functional data with cycles.
method Functional linear structural equation model with a low-dimensional causal embedded space.
result The proposed model is causally identifiable under standard assumptions.
Bayesian method learns graph structures from Gaussian data efficiently.
problem Scalability issue in Bayesian Gaussian graphical model inference.
method Marginal pseudo-likelihood, birth-death and reversible jump MCMC algorithms.
result Efficient graph structure learning for large graphs with over 1,000 nodes.